Because of the large fixed cost of running pipes to everyone's home, natural gas is locally provided by a natural monopoly. Suppose demand is Q = 240 2 P and marginal revenue is M R = 120 Q . Suppose marginal cost is $20, and the fixed cost of setting up the natural gas pipelines is $4,000. 1. If the monopolist is unregulated, it will set the price of natural gas at P = 2. At that price, it will sell a quantity Q = 3. And make a profit of What regulatory price maximizes social welfare (the sum of consumer and producer surplus)? At the regulatory price that maximizes social welfare, what is the monopolist's profit? (Enter a negative number if it's a loss.) To ensure sustainable operations, the regulator wants to set the price of natural gas to where the utility would no longer make a loss (but not more than that). To calculate the price at which profit is equal to zero, which equation will the regulator need to solve